Multipath interference in the time domain may be represented by the superposition of an initial version of a signal of interest (SOI) with multiple delayed and filtered versions of the same signal. The delayed and filtered versions of the SOI result from reflections and other irregularities. When viewed in the frequency domain, multipath interference can be modeled as a comb filter placed somewhere in the transmission path of an SOI.
FIG. 1 is a block diagram of a prior art signal processing system that attempts to reduce the effects of multipath interference on a received signal. This system places an adaptive transversal (or FIR) filter in the receiver signal path whose function is to undo linear errors caused by multipath interference.
Equations 1 through 4 below provide the mathematical foundation for a prior art adaptive transmission channel equalizer based on a Constant Modulus Algorithm (CMA). CMA refers to the type of error estimate used to adjust the transversal filter coefficients. These equations specifically refer to a form of CMA referred to as CMA 2-2 (after Dominique Goddard), but the discussion can be generalized to other forms of CMA known in the prior art.y(k)=WT(k)X(k)   Eq. 1W(k+1)=W(k)−μecm(k)X*(k)   Eq. 2ecm(k)=[|y(k)|2−R2]y(k)   Eq. 3R2=E{|y(k)4}/E{″y(k)|2}  Eq. 4
In equations 1 through 4 above, X(k) is a vector of input history at time k, y(k) is the scalar output value from the adaptive filter, W(k) is a vector of filter coefficients, ecm[k] is the Constant Modulus Error Estimate, which is based on the CMA 2-2 algorithm, R2 is a constant that is dependent upon the data modulation method used, and represents the scaling necessary to match the adaptive filter output to the thresholds of the data demodulator. For Constant Modulus modulation methods such as frequency modulation (FM), this expression reduces to R2=Ro2, where Ro=E{|y(k)|}. μ is a step size parameter that adjusts the extent to which coefficients are changed at each time step. Each next set of coefficients W(k+1) is determined based on the previous coefficient values W(k) and an estimate of the gradient of the error of the filter output modulus with respect to the transversal filter tap weights (coefficients).
In prior art system 100 of FIG. 1, an input signal is received by front end block 10. The front end serves as an interface between the outside world and the system of interest. A typical front end may incorporate a signal conditioning function and some type of tuning function. Signal conditioning is usually applied to match the incoming signal from the outside world to the system of interest, in order to enhance system dynamic range and signal to noise ratio (an example is use of an AGC function in the RF front end of a radio receiver). Tuning usually consists of combining a frequency selective function with a frequency shifting function, where the shifting function is used to shift the range of frequencies over which the frequency selectivity occurs.
The output of front end 10 feeds into power normalization block 20. In some systems, power normalization may be performed directly by front end 10 (in the AGC if present). In such systems, a separate power normalization stage is not required. However, it is often the case the output of front end 10 may still have an average signal power that varies considerably with time. In these cases, a separate power normalization function is applied.
FIG. 1 shows power normalization 20 located ahead of the ADC 30. Power normalization 20 may be accomplished by an analog AGC. In system 100 of FIG. 1, the power normalized signal (the output of power normalization block 20) is then digitized by ADC 30 and applied to the input of adaptive transversal filter 40. Eq. 1 defines the signal processing of transversal filter 40 given the input data and coefficient vectors. The output of adaptive transversal filter 40 splits into two paths, a signal path and a control path. The signal path output is demodulated by demodulation block 70 in a manner that represents the inverse of the method used to originally modulate the data. After demodulation, the demodulated signal may also be decoded, if the original modulating signal was encoded in some manner. The output of demodulator 70 is the recovered data signal of interest.
The control path output feeds back into Constant Modulus (CM) Error Estimation block 60. CM error estimation block 60 determines an error cost function in accordance with Eq. 3, which effectively is the difference between the modulus of the output of adaptive filter 40 and a constant value R2 (as defined in Eq. 4). The result of this determination is the error estimate signal ecm(k). The error estimate signal ecm(k) (the output of CM error estimation block 60) feeds into coefficient determination block 50. Coefficient determination block 50 determines coefficient signal updates in accordance with Eq. 2. The coefficient signal values are updated based on the error estimate signal ecm(k), the current coefficient signal values W(k), the adaptation step size μ, and the conjugated input data signal X*(k). When functioning as intended, the coefficient value signals determined at succeeding time steps change in a direction that tends to minimize the error cost function.
Prior art system 100 of FIG. 1 assumes that the transmitted SOI has a constant modulus property. When such a signal is subject to multipath interference (during transmission, for example), the received signal will no longer have a constant modulus property. (The comb filter behavior caused by multiple reflections destroys the constant modulus behavior). CM error estimation block 60 of prior art system 100 in conjunction with coefficient determination block 50 determines coefficient signals for transversal filter 40 that attempt to force the output of transversal filter 40 to have a constant modulus property. Algorithms that accomplish this behavior are referred to as CMA (constant modulus algorithms).
For additional background reference is made to the following:
NumberTitleInventorDateU.S. Pat. No.CMA-Based AntennaYukitomo,May 25, 19995907303Systemet al.U.S. Pat. No.Technique for ImprovingWerner,Sep. 15, 19985809074the Blind Convergence ofet al.an Adaptive EqualizerUsing a TransitionAlgorithmU.S. Pat. No.GeneralizedWerner,Aug. 17, 19995940440Multimoduluset al.Technique for BlindEqualizationU.S. Pat. No.Reducing MultipathTingleyDec. 9, 19975697084Fading UsingAdaptive FilteringU.S. Pat. No.Method and Device forGodardJan. 5, 19824309770Training an AdaptiveEqualizer by Means of anUnknown Data Signal ina Transmission SystemUsing DoubleSideband-QuadratureCarrier ModulationU.S. Pat. No.Adaptive EqualizingHwangApr. 9, 19965506871System for Digitalet al.CommunicationsEP 0 854 589Adaptive AntennaAkaiwa,Jul. 22, 1998A2Diversity Receiveret al